Question: $(18-40i)-(-9+2i)=$ Express your answer in the form $(a+bi)$.
Solution: Background Complex numbers can be added or subtracted by separately adding or subtracting their real and imaginary terms. To add or subtract complex numbers: Expand parentheses (attending to minus signs outside of parentheses if necessary) Combine all real terms (terms that do not contain $i$ ), and add or subtract them. Combine all imaginary terms (terms that contain $i$ ), and add or subtract them. Combining Like Terms $\begin{aligned} ({18}{-40}i)-({-9}+{2}i)&={18}{-40}i+{9}-{2}i \\\\ &={18}+{9}{-40}i-{2}i \\\\ &={27}{-42}i \end{aligned}$ Summary $({18}{-40}i)-({-9}+{2}i)={27}{-42}i$